Homework Statement:
Given the plane: 4x - 2y +8z = 8,
Find Parametric equations of the line of intersection of the given plane and the xz-plane.

The answer for the question is: x = 2 +2t ; y = 0, z = -t

I don't understand how to get to this answer and I am going to be tested on this type of question. Can anyone help me understand this please?
Relevant Equations:
x = x1 + at
y = y1 + bt
z = z1 +ct
Sorry for the really messy work I know I have a problem.

The other questions that the problem asked before the one I need help with are as follows:
Find the intercepts and sketch the plane.
Find the distance between the plane and the point (1,2,3)
Find the angle between the plane and the xz plane

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BvU
Homework Helper

I don't understand how to get to this answer
Aren't you thinking this through too deeply ?
Is it clear that points on the intersection with the xz-plane have y = 0 ? From there $$4x - 2y +8z = 8 \ \& \ y = 0 \Rightarrow 4x + 8z = 8 \Rightarrow x + 2z = 2$$ and any choice for a parameter will do. You say 'the answer', but it's just an answer out of many. Other examples: x = t, y = 0 , z = (t-2)/2, or
z = t , y = 0, x = 2 - 2t etc, etc.

LCKurtz
Homework Helper
Gold Member
A general method to find the line of intersection of two planes is:
1. The cross product of the two normals to the planes gives a direction vector for the line.
2. Find any point on both planes to use with the direction vector. You can usually set one variable = 0 and solve the remaining two equations for the other coordinates of the point.